Electrostatics of two intersecting conducting cylinders

An exact result for the perturbed electric potential disturbed by a conductor formed by a pair of intersecting, conducting infinitely long cylinders placed in an arbitrary potential field is provided. Applying the idea of Kelvinʹs inversion repeatedly, the general solution for the potential function is derived for the case when the two cylinders intersect at a vertex angle π/n (n an integer). The exact expression for the potential is presented as a theorem followed by a simple proof. The corresponding expression in complex form is also given. The general result is then used to find the image systems for various imposed potentials in a straightforward fashion.